Zazzle is a POD or Print on Demand printer, meaning they only print the item after it is purchased.
Zazzle can offer millions of designs by talented, and no so talented artists all over the world simply because they do not print them until after they are paid for.
You do not need to be an artist to have a shop on zazzle, you just need to be creative, and have a point of view no one else has. That is to say you cannot simple take am image or idea you found online or in a movie or book, and use it. You must come up with the idea all on your own and make it all on your own.
For more on what is legal and what is not legal check out the What can I sell on zazzle page.